Greek Gift

Recently, my opponents have been playing Greek gift sacrifices against me. Many of those times I didn't play an opening which immediately led to a Greek gift sacrifice, but somehow transposed. Do you have any suggestions on how to avoid the Greek Gift or which opening/openings to play to avoid it?

I don´t know if your question has really an answer, but I don´t face greek gifts playing the slav against queen pawn oppenings, for instance. 
Or even the sicilian najdorf, as well, against king pawn. 

As long as you have a knight on f8, you should be fine.

The Greek Gift Sacrifice is a middlegame tactic, not opening theory.

Obviously it is more common in certain openings, especially those where Black does not fianchetto his kingside.

In fact, there is a 400 page book written on the Greek Gift Sacrifice from a Correspondence Chess Master, and you'll notice in the index of openings that it occurs by far more often in the Colle System or French Defense than any other opening, but that doesn't make those two openings bad for Black.  I have played the French all my life and have not fallen for any lines that lead to a legitimate Greek Gift Sacrifice.  I have had opponents try to play it, and gotten my King out there to g6, but in cases that were at best a draw and many times losing for White.

You need to understand the idea, not try to associate it with certain openings.  It's not the opening that allowed it to happen.  It's the poor play afterwards!

I agree with @thrillerfan, you don't have to change your repertoire just because you keep falling for a trap, always be aware of Bxh7+ sacrifices and calculate all the lines in it:

This is the kind of position where it works, but there is smth both of you and your oppoent should be aware of, 

Which is the avaliabilty of defending the mating threats

Bishop on e7 prevents the greek gift.

Yes as well as h6 and g6

While common defensive mechanisms like having the Bishop on e7 or Knight on f6 or advancement of the pawns in front of your king might prevent the Greek Gift, it may lead to other issues instead.  So do not just assume that advancing a pawn or putting your Bishop on e7 solves all problems.  For example, if White has not castled and has played h4, then despite a Bishop on e7, it might still work.  You have to account for Qd3 instead of Qh5.  You have to account for cases where Ng5+ Bxg5 hxg5 is check because the White Rook is still on h1.

The best thing you can do is get the book "Sacking the Citadel" by Jon Edwards and put some hard time into studying it.

And if you play the Colle or French from either side, it will also highly benefit you simply via exposure to two openings as well.

It goes into great detail all of the various ways to execute and prevent the Greek Gift, like the ...Nf5 defense, just to name an example.

Thanks for all the tips!